First published in Latin in 1699, John Craige’s _Theology _represents a rare early attempt to introduce mathematical reasoning into moral and theological dispute. Craige’s effort to determine the earliest possible date of the Apocalypse earned him ridicule as an eccentric and a crank. Yet, Richard Nash argues, the intensity of the response to Craige’s work testifies to how widely felt the conflict was between the old and newly emergent notions of probability.
Recent technical developments in the logic of nominalism make it possible to improve and extend significantly the approach to mathematics developed in Mathematics without Numbers. After reviewing the intuitive ideas behind structuralism in general, the modal-structuralist approach as potentially class-free is contrasted broadly with other leading approaches. The machinery of nominalistic ordered pairing (Burgess-Hazen-Lewis) and plural quantification (Boolos) can then be utilized to extend the core systems of modal-structural arithmetic and analysis respectively to full, classical, polyadic third- and fourthorder number (...) theory. The mathenatics of many structures of central importance in functional analysis, measure theory, and topology can be recovered within essentially these frameworks. (shrink)
In the physical sciences a realist ontology rests on our ability to demonstrate the actual and real nature of material entities. Realist metaphysics of social entities, most influentially Bhaskar's critical realism, attempt to provide a related philosophical foundation for the social sciences. This paper examines the central issue of what is real about society it concludes that social relations and the organisations they constitute do exist and discusses the conditions of their demonstration. Realist interpretations of Bourdieu's theories are given particular (...) attention in an argument that accepts the necessity of social realism but remains cautious about the development of methodologies able to provide effective demonstration. (shrink)
This paper explores the American bankruptcy system -- especially the Chapter 11 code -- which since 1978 has allowed insolvent companies the opportunity to restructure and reorganise with the benefit of court protection from creditors. Particular attention is focused on asbestos companies, such as Johns--Manville, which have been among the most consistent and controversial filers for bankruptcy under Chapter 11. The history of asbestos and Chapter 11 is explored, against the backdrop of the burgeoning asbestos crisis, caused by increasing mortality (...) and litigation. Some of the business and ethical issues involved are highlighted by examining in detail a recent bankruptcy (Federal Mogul/T&N in 2001) that has implications in both Britain and America. Chapter 11 bankruptcy is evaluated, particularly in the light of the trend towards similar mechanisms of insolvency in the UK, Europe and the rest of the world. It is concluded that, certainly as regards the experience with asbestos, Chapter 11 offers an inefficient and inequitable method of rehabilitating or rescuing failing businesses. (shrink)
“It is important to stress that a variety of positions with respect to feminism, nation, religion and identity are to be found in Anglophone Arab women’s writings. This being the case, it is doubtful whether, in discussing this literary production, much mileage is to be extracted from over emphasis of the notion of its being a conduit of ‘Third World subaltern women.’” Building on GeoffreyNash’s statement and reflecting on Deleuze and Guattari’s conceptualization of minor literature and Gloria (...) Anzaldua’s Borderland, we will discuss in this paper how the writings of Arab Anglophone women are specific minor and borderland narratives within minor literature through a tentative localization of Arab women’s English literature into distinct and various categories. By referring to various bestselling English works produced by Arab British and Arab American women authors, our aim is to establish a new taxonomy that may fit the specificity of these works. (shrink)
The creation story in Genesis speaks of humankind being given dominion over nature. Does this support the view that nature has solely instrumental value, and is of worth only insofar as it serves the necessities and conveniences of the human species? Does dominion amount to unfettered domination here? An interpretation of the story is advanced employing procedures of practical criticism. Three central images are focussed on: Adam's being given dominion over the other creatures, his naming of them, and his being (...) made in God's likeness. It is argued that these images, in their qualification and enrichment of each other, develop the idea that animals are of worth independently of their usefulness to us. Other key parts of the Bible, that at first may seem to promote unfettered domination, are shown to be more properly read as supporting an animal-benign religious ethics. (shrink)
This paper argues that Adolf Gr nbaum's evaluation of the scientific status of psychoanalysis is marred by its failure to locate Freud's notion of natural science. Contrary to his claims, Griinbaum does not assess Freud's theory on Freud's own terms. The presuppositions that Griinbaum brings to the question of the scientific status of psychoanalysis are problematic and his criticisms and methodological restrictions may not be defensible when psychoanalysis is taken to develop methodologically out of medical science rather than out of (...) physics. I question the adequacy of the epistemological and methodological norms that Griinbaum brings to his analysis and I examine his arguments against the scientific credibility of Freud's theoretical claims. I argue that Griinbaum fails to consider the tension between clinical practice and psychoanalytic theory, ignores the evolution of Freud's thought and distorts and simplifies the complexity of the domain under investigation. Therefore his conclusions regarding the scientific credibility and evaluation of psychoanalysis are questionable. (shrink)
Supplemented by interviews with four of the major participants in the debate--Ray Jackendoff, George Lakoff, Paul Postal and John Robert Ross--this book shows that the paradigm which has dominated American linguistics for the last twenty ...
Chambliss, J. J. The guardian, Plato.--Proussis, C. M. The orator, Isocrates.--Rexine, J. E. The Stoic, Zeno.--Kibre, P. The Christian, Augustine.--Donohue, J. W. The Scholastic, Aquinas.--Schacht, F. E. The classical humanist, Erasmus.--Clauser, J. K. The pansophist, Comenius.--Benne, K. D. The gentleman, Locke.--Ballinger, S. E. The natural man, Rousseau.--Bibby, C. The scientific humanist, Huxley.--Nyberg, P. The communal man, Marx.--Holmes, B. The reflective man, Dewey.--Bantock, G. H. The cultured man, Eliot.--Friedman, M. The existential man, Buber.--Aschner, M. J. M. The planned man, Skinner.
It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice (...) in the form 'each according to her basic needs and above this level according to her relative bargaining power'. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls' original position. (shrink)
We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to (...) explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)
In a recent article, McClennen (2012) defends an alternative bargaining theory in response to his criticisms of the standard Nash bargaining solution as a principle of distributive justice in the context of the social contract. McClennen rejects the orthodox concept of expected individual utility maximizing behavior that underlies the Nash bargaining model in favor of what he calls full rationality, and McClennen’s full cooperation bargaining theory demands that agents select the most egalitarian strictly Pareto-optimal distributional outcome that is (...) strictly Pareto-superior to the state of nature. I argue that McClennen’s full cooperators are best described as reasonable agents whose rationality is constrained by moral considerations and that McClennen’s bargaining theory is moralized in this regard. If, by contrast, the orthodox concept of rationality is assumed and plausible assumptions are made about human nature and social cooperation, then a modified version of the standard Nash bargaining solution, which I call the stabilized Nash bargaining solution (Moehler 2010), is justified. From the perspective of rational agents, the stabilized Nash bargaining solution can accommodate McClennen’s criticisms of the standard Nash bargaining solution in the context of the social contract and, for such agents, it can serve as a principle of distributive justice in deeply morally pluralistic societies. (shrink)
The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in (...) terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)
In this study we introduce two new properties, the Midpoint Outcome on a Linear Frontier (MOLF) and Balanced Focal Point (BFP) properties, to replace the Weak Pareto Optimality (WPO), Symmetry (SYM) and Independence of Equivalent Utility Representations (IEUR) properties in the axiomatic characterizations of the two most prominent solution concepts, namely the Nash and Kalai/Smorodinsky solutions, respectively.
Within a formal epistemic model for simultaneous-move games, we present the following conditions: belief in the opponents’ rationality, stating that a player believes that every opponent chooses an optimal strategy, self-referential beliefs, stating that a player believes that his opponents hold correct beliefs about his own beliefs, projective beliefs, stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and conditionally independent beliefs, stating that a player believes that opponents’ types choose (...) their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy. We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped. (shrink)
We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (J Econ Theory 21: 75–106, 2005, Theorem 3.3) and show that for any weakly responsive couples market, there always exists a “double stable” matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets, the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that (...) assigns all double stable matchings is neither monotonic nor Nash implementable. (shrink)
Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition âstrong rationalizabilityâ), then the true (or actual) strategy profile is path equivalent to a (...)Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C8 , the set of profiles that survive the iterative deletion of inferior profiles. (shrink)
This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.
In this paper we deal with the extension of Nash bargaining theory to nonconvex problems. By focussing on the Social Welfare Ordering associated with a bargaining solution, we characterize the symmetric Nash Bargaining Solution (NBS). Moreover, we obtain a unified method of proof of recent characterization results for the asymmetric single-valued NBS and the symmetric multivalued NBS, as well as their extensions to different domains.
The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.
In game theory, the word ‘game’ is used to describe any interdependence between interacting parties, and the Nash equilibrium is a prominent tool for analysing such interactions. I argue that the concept of the Nash equilibrium may also be used in non-gaming contexts. An individual is in a Nash equilibrium if his or her beliefs are consistent with his or her actions. Given that discordance between beliefs and behaviour is a typical cause of psychiatric disorders, individuals who (...) are not in a Nash equilibrium are likely to be affected by such disorders. In this regard, the concept of the Nash equilibrium could aptly be introduced into the medical practitioner’s vocabulary for describing a patient’s mental health status. (shrink)